Find the area of a polygon with the given vertices? A(1, 4), B(2, 2) C(7, 2), D(4, 4) Please show work.
Consider that the polygon ABCD is composed of the triangle ABC and ACD.
To find the area of a triangle whose vertices coordinates are given we can use the Cramer's Rule, described in: Finding the area of a triangle using the determinant of a matrix
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S=30
Repeating the points A(1,4) B(2,2) C(7,2) D(4,4)
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To find the area of the polygon with the given vertices A(1, 4), B(2, 2), C(7, 2), and D(4, 4), you can use the Shoelace Formula. Here's how to do it:
 Write down the coordinates of the vertices in clockwise order.
 Repeat the first coordinate at the end to complete the cycle.
 Multiply each pair of coordinates: (x1 * y2)  (x2 * y1) for each consecutive pair.
 Add up all the results obtained in step 3.
 Take the absolute value of the sum from step 4.
 Divide the result by 2 to get the area of the polygon.
Using the coordinates given:
A(1, 4), B(2, 2), C(7, 2), D(4, 4), A(1, 4)
 Coordinates in clockwise order: A(1, 4), B(2, 2), C(7, 2), D(4, 4), A(1, 4)
 Multiply each pair of coordinates:
(A(1, 4) \times B(2, 2) = (1 \times 2)  (4 \times 2) = 2 + 8 = 6)
(B(2, 2) \times C(7, 2) = (2 \times 7)  (2 \times 2) = 14  4 = 10)
(C(7, 2) \times D(4, 4) = (7 \times 4)  (2 \times 4) = 28  (8) = 36)
(D(4, 4) \times A(1, 4) = (4 \times 1)  (4 \times 1) = 4  4 = 8)
 Add up the results:
(6 + 10 + 36 + (8) = 44)

Take the absolute value: (44 = 44)

Divide by 2: (44 \div 2 = 22)
The area of the polygon is (22) square units.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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